With few avenues left for winning a comprehensive budget deal that can reverse the across-the-board spending cuts that took effect over the weekend, President Obama has begun reaching out to senators in a bid to isolate Republican leaders in Congress and force a compromise.

In conversations last week with Sens. Lindsey Graham of South Carolina and John McCain of Arizona, both Republicans, and in a wider outreach to rank-and-file members of Congress that a top White House official said began this weekend, Obama hopes to build a broad consensus on deficit reduction that includes new revenue, despite the uncompromising stance of Republican leaders in the House and the Senate.

“Our hope is that as more Republicans start to see this pain in their own districts, that they will choose bipartisan compromise over this absolutist position,” Gene Sperling, the director of the president’s National Economic Council, said Sunday on NBC’s “Meet the Press.”

Appearing immediately before him on the program, Speaker John Boehner reinforced his opposition to any deal to reverse the cuts in military and domestic programs — $85 billion this year and nearly $1 trillion over 10 years — that includes raising new revenue. But he did leave open a narrow path to a comprehensive budget agreement that could restore at least some of the money at some point.

Boehner said Obama had already raised nearly $1 trillion to finance his health care program and, in January, won $650 billion from tax increases on high incomes.

But Boehner offered some hope that the budget process — which begins this week with the expected passage by the House of a spending measure, known as a continuing resolution, to keep the government operating for the rest of the year — could still end in a broad agreement that lowers the deficit, overhauls the tax code and undoes at least some of the automatic spending cuts.

“I don’t think anyone quite understands how it gets resolved,” he acknowledged. “After we do our continuing resolution, we’ll begin to work on our budget. The House has done a budget every year that I’ve been speaker. The Senate hasn’t done a budget for four years. They’ve committed to do a budget this year. ... And out of that discussion and out of that process, maybe we can find a way to deal with our long-term spending problem.”

Senate Minority Leader Mitch McConnell of Kentucky, appearing on CNN’s “State of the Union,” gave no indication he was willing to undo the automatic cuts with new revenue, only with cuts in other parts of the budget.

“We’re willing to talk about reconfiguring the same spending over the next several months,” he said.

The White House was left to hope that rank-and-file senators can build momentum for a bipartisan deal that isolates Republican leaders and exerts pressure that cannot be resisted.

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